Given two displacement vectors A⃗ =(3.00iˆ−4.00jˆ+4.00kˆ)mA→=(3.00i^−4.00j^+4.00k^)m and B⃗ =(2.00iˆ+3.00jˆ−7.00kˆ)mB→=(2.00i^+3.00j^−7.00k^

Question

Given two displacement vectors A⃗ =(3.00iˆ−4.00jˆ+4.00kˆ)mA→=(3.00i^−4.00j^+4.00k^)m and B⃗ =(2.00iˆ+3.00jˆ−7.00kˆ)mB→=(2.00i^+3.00j^−7.00k^)m, find the displacements and their magnitudes for (a) C⃗ =A⃗ +B⃗ C→=A→+B→ and (b) D⃗ =2A⃗ −B⃗ D→=2A→−B→.

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RobertKer 3 years 2021-09-05T13:18:08+00:00 1 Answers 61 views 0

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  1. Cherry
    0
    2021-09-05T13:19:20+00:00
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    Answer:

    Displacement C = (5.00iˆ – 1.00jˆ – 3.00kˆ) m

    Magnitude = 5.92 m

    Displacement D = (4.00iˆ−11.00jˆ+15.00kˆ) m

    Magnitude = 19.03 m

    Explanation:

    Vector A = (3.00iˆ−4.00jˆ+4.00kˆ) m

    Vector B = (2.00iˆ+3.00jˆ−7.00kˆ) m

    a) Vector C = A + B = (3.00iˆ−4.00jˆ+4.00kˆ) + (2.00iˆ+3.00jˆ−7.00kˆ)

    Vector addition is done component by component, that is, do î component, then j component and k component

    C = (5.00iˆ – 1.00jˆ – 3.00kˆ) m

    Magnitude of C = √[(5²) + (-1)² + (-3)²] = √(35) = 5.92 m

    b) Vector D = 2A – B

    D = 2(3.00iˆ−4.00jˆ+4.00kˆ) – (2.00iˆ+3.00jˆ−7.00kˆ) = (6.00iˆ−8.00jˆ+8.00kˆ) – (2.00iˆ+3.00jˆ−7.00kˆ) = (4.00iˆ−11.00jˆ+15.00kˆ)

    Magnitude of D = √[(4²) + (-11)² + (15)²] = √(362) = 19.03 m

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